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Summary

Summary. On-axis (x=y=0) specifications, normal, b n , and skew, a n Integrated quadrupole < 50 G Integrated sextupole < 75 G/cm Integrated octupole < 40 G/cm 2 Off-axis specifications 1 st integral of B y < 100 + 50*|x| G*cm, |x|<2.5 cm

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Summary

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  1. Summary • On-axis (x=y=0) specifications, normal, bn, and skew, an • Integrated quadrupole < 50 G • Integrated sextupole < 75 G/cm • Integrated octupole < 40 G/cm2 • Off-axis specifications • 1st integral of By < 100 + 50*|x| G*cm, |x|<2.5 cm • 1st integral of Bx < 40 + 75*|x| G*cm, |x|<2.5 cm • 2nd integral of By < 1.5e4+1e4*|x| G*cm2, |x|<2.5 cm. • 2nd integral of Bx < 5e3+1e4*|x| G*cm2, |x|<2.5 cm • 1st integral deriv. < 50+150*|x| G; |x|<2.5 cm, • Peak field transverse roll-off • dBy/dx < 11000+5500*|x| G/cm, |x|<2.5 cm (BL12) • d2By/dx2 < 15000+20000*|x| G/cm2, |x|<2.5 cm (BL12) • Accelerator physics group will review fields, once the ID is designed. • Accelerator physics group will review magnetic measurements plan.

  2. q L*q/2 q/2 L=1.1m 1st integral (I1) specification, x=y=0 • Feedback off: global orbit shift less than 10% beam size • Horizontal: Dx(s) ~ sqrt(b(s)b0)*I1/Br < 40 mm • I1h < 43 G*cm • Vertical: Dy(s) ~ sqrt(b(s)b0)*I1/Br < 3 mm • I1v < 11 G*cm • Feedback on; beam fixed at BPMs about L=1.1 m up and downstream of ID; local orbit shift less than 10% of beam size and angle • Horizontal: • Dx = L* I1/Br/2 < 40 mm … I1h < 727 G*cm • Dx’ = I1/Br/2 < 5 mrad … I1h < 100 G*cm • Vertical: • Dy = L* I1/Br/2 < sqrt(2.5e-3*.018mm*mrad*1.6m)=8.5 mm … I1v < 155 G*cm • Dy’ = I1/Br/2 < 0.1*sr’ = 1 mrad … I1v < 20 G*cm • SLS specified 20 G*cm and got 26 G*cm. • BL12 spec: • I1h < 100 G*cm; I1v < 40 G*cm BPM ID BPM

  3. Field integral specifications, x=y=0 • Gradient • BL4&7: 50 G • ALS W11: 50 G • SLS IVUN: 50 G • BL12&13: 50 G • Sextupole • BL4&7: 100 G/cm • ALS W11: 50 G/cm • SLS IVUN: 60 G/cm • BL12&13: 75 G/cm • Octupole • BL4&7: No specification, (150 G/cm2 for BL11) • ALS W11: 10 G/cm2 • SLS IVUN: 100 G/cm2 (measured 9 G/cm2) • BL12&13: 40 G/cm2 (tracking studies indicate that 200 G/cm2 would start to be a problem)

  4. Skew gradient • 50 Gauss would generate ey/ex = 0.0094% • In operations now, ey/ex = 0.047% (8.5 pm) • With all skew quads off, now, ey/ex = 0.27%

  5. For BL12 & 13: 100 + 50*|x| G*cm, |x|<2.5 cm; (ALS extended to 25 mm)

  6. Multipole tracking

  7. 1st integral derivative specification • BL4&7: 200+300*|x| G; |x|<2.5 cm, y=0 • ALS W11: 50+50*|x| G; |x|<2 cm • SLS IVUN: 50 G; |x|<2 cm • For BL12&13: 50+150*|x| G; |x|<2.5 cm

  8. 2nd field integral specification • BL4&7: 1e5+1.5e5*|x| G*cm2; |x|<2.5 cm, y=0 • From BL11 specs. • to control orbit • ALS W11: 1e4+5e3*|x| G*cm2; |x|<2 cm • for dynamic aperture; “somewhat hand-wavey” • SLS IVUN: 1.6e3 @x=y=0; 3.2e3; x=+/-1mm, y=+/-.5mm • to control orbit, (I guess, given range in x, y.) • BL12 considerations: • 2nd integral intrinsic to asymmetric device = Bpeak/k2 = 1.23e3 G*cm2 • 2nd integral from +/- 1rst integral spec on ends of ID = 1rst*length = 1.5e4 + 7.5e3*|x| G*cm2, |x|<2.5 cm • Global orbit control: 2nd integral, I2, gives orbit distortion amplitude of x(s) = (I2/Br)*sqrt(b(s)/b0)/(2sinpn) ~ I2/Br < 10% of beam size = (40, 3) mm, (x, y). This gives I2< (4e4, 3e3) G*cm2, (x, y). • With orbit feedback: I2 generates an angular shift of about I2/(3*L*Br) < 0.1*s’ = (5,1)mrad. L=1.5 m = ID length. This gives I2< (1.8e4, 4.5e3) G*cm2, (x, y). • BL12 spec: • I2h< 1.5e4+1e4*|x| G*cm2, |x|<2.5 cm. • I2v< 5e3+1e4*|x| G*cm2, |x|<2.5 cm.

  9. Pole width; transverse field roll-off • BL4&7: field roll-off specs., 1rst & 2nd deriv. • ALS W11: kx < 6.5 1/m • SLS IVUN: pole width >= 42 mm

  10. Field roll-off specification Field integral from transverse field roll-off: In BL11 max(dBy/dx)=0.6*max(By)/gap, which for BL12 would give max(dBy/dx)=11000 G/cm, so this specification should be achievable, even with narrow poles.

  11. Field roll-off specification, 2nd derivative Field integral from transverse field roll-off: This constraint is tighter than necessary, because the multipoles are known to be only odd normal multipoles. For example, the quadrupole term of 50 Gauss at x=0 would only make a b-beat of 0.2 %. I’ll relax the constraint: This constraint is still about three times tighter than the one used for BL4&7. In BL11 max(d2By/dx2)=max(By)/gap2, which for BL12 would give max(d2By/dx2)=33000 G/cm2, so this specification should be achievable, even with narrow poles.

  12. SLS IVUN specs.

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